Classes of operators preserved by extensions or liftings
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2018Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International
Publicado en
Journal of Mathematical Analysis and Applications (2018) Vol.462, Issue 1, pp. 471-482
Editorial
Academic Press Inc.
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Palabras clave
Extending operators
Lifting operators
Operator ideal
Resumen/Abstract
A standard way to obtain extensions (resp. liftings) of operators is by making the so-called operations of push-out (resp. pull-back). In this paper we study the preservation of some classes of operators associated with an operator ideal Aunder push-out extensions or pull-back liftings. We show several examples of classical operator ideals whose associated classes are preserved, we prove that the preservation of those classes under push-out extension or pull-back lifting implies that the space ideal of Asatisfies the 3-space property, and we derive some results for Athat are useful in the study of commutative diagrams of operators.
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